A note on multiple comparison procedures for detecting differences in simply ordered means

AbstractIntheone-wayANOVA,weconsiderproceduresthatdetermine whether m i ¼ m j orm i om j whenthemeans are known a priori to be nondecreasing. It is known that the one-sided Studentized range test(OSRT) controls the familywise error rate, but the one-sided least significant difference test has largerpowers.Weshowthatforbalanceddesigns,thefamilywiseerrorrateofthelatterislargestwhenallofthemeansareequalbutone.Thisleadstoamodificationoftheone-sidedleastsignificantdifferenceprocedurethat controls familywise error rate andhas larger powers than the OSRT. Some recommendations forunbalanceddesignsarealsogiven.r 2005ElsevierB.V.Allrightsreserved. Keywords: Analysisofvariance;Isotonicinferences;Order-restrictedinferences;Simultaneousinferences;Familywiseerrorrate;Totalorder 1. IntroductionIn some comparisons of treatment means, the experimenter may believe a priori that the kpopulation meansare ordered in a certain way. For instance, if the treatments are increasingdosagelevels,whichareinareasonablerange,thenonemaybelievethatthemeanresponsesarenondecreasing(orpossiblenonincreasing).Inthisnote,multiple-comparisonprocedures,which